Individual Student Information and Differentiation StrategiesConsult the Lesson Rational Reflection and the http://www.secondarydifferentiation.weebly.com

#1 Student - Student with Special Education Needa. Name: Vincent b. Eligibility: 504 for emotional issues when he doesn't understandc. Identity: 9th grade student. EL4 with primary language of Vietnamese. Visual learner who needs to see the work being done and then perform the task. Needs to be reassured that he is performing the activity correctly even when he is not having difficulty.d. Goals: Vincent wants to go to college and enjoys drawing.e. Readiness: Vincent has one of the highest grades in class and is proficient in the material being covered. f. Interest: He enjoys drawing when he has free time. g. Learning Profile: Visual learner, he needs to see the work being done to understand how the steps are related.h. Differentiation: Vincent can complete the tasks given in class and only requires reassurance that he is doing the work correctly.

Content: No content change required

Process: Needs to be checked up on regularly to ensure that he feels confident in his method and to reinforce the knowledge that he is doing the work correctly.

Product: Completes the same assessments as the rest of the class.

Affect: Completes all of the normal class activities with the class. Is allowed to complete his assessments in the collaborative area so that he doesn’t get distracted during assessments.

Learning Environment: Is seated in the front row of class to allow the instructor to quickly check on his work and understanding during class. Is seated next to a friend from middle school who understands how to calm him down if he becomes agitated during a task.

i. Assessment: The unit has daily formative assessments of the students understanding of the material. Vincents specific needs require that he is monitored regularly throughout the unit to ensure that he understands the material being covered daily. This monitoring will ensure that he understands the material and is making progress.

#2 Student - English Language Learnera. Name: Luisb. ELL Level: EL4 c. Identity: 11th grade student. EL4 with primary language of Spanish. Is easily distracted during class. Does not place great value in participating in classroom discussions or activities. Is taking the class to fulfill his requirement of two years of math.d. Goals: Student has already passed the CAHSEE and wants to work for the police department.e. Readiness: Student is taking Algebra 1 for the 2nd time, he completed Sheltered Algebra 1 with a D last semester. He didn’t want to move on to geometry. f. Interest: Student is distracted in class and feels that he understand all of the material already. Student has 10 absences this semester.g. Learning Profile: Student needs to work on the hands on with the material to remember how the operations are performed.h. Differentiation:.

Content: All students are given graphic organizers at the start of unit to covers the terms and operations that will be used. All material is presented both visually and vocally to students to ensure that they can see and hear the information.

Process: Students are given opportunities everyday to discuss with their tablemates the problems and their methods for solving the systems of equations.

Product: Completes the same assessments as the rest of the students.

Affect: Completes all normal class activities with the class. Considering his designation as an EL4 effort is made to ensure that he is understanding all material during instruction. Since he has previously completed Algebra 1 he normally only needs a reminder of the steps required to solve a problems once.

Learning Environment: Student had back surgery over the summer and is allowed to arrive up to 3 minutes late to class. Student is allowed to take his assessments in the collaborative area so that he doesn’t get distracted and can ask for help if needed.

i. Assessment: Student has previously completed Algebra 1 with a D and is currently repeating the unit to cover required 2 years of math education. He is expected to complete all normal assessments with the class. He is checked up on regularly to ensure that he is understanding the material under discussion.

#3 Student – Low Level Studenta. Name: Cody b. Need: Cody needs extensive remediation in mathematics. He has forgotten or never mastered many areas of basic mathematical knowledge. We need to check his work when he performs long division on multiplication. Regular checks are made throughout the lesson to ensure that he is understanding the material and process. c. Identity: 9th grade student. Single mother family. English is the primary language at home. Is on the freshman cross country team.d. Goals: We are working to ensure that the student passes this class and understands all material. He needs to be reminded to stay on task and to persevere in working on a problem when he encounters a problem that he can not easily solve.e. Readiness: The student is below the expected readiness level of this course and needs remediation on multiple mathematical topics. f. Interest: Student is on the cross country team and wants to maintain a C in the class. g. Learning Profile: The student needs to work with the problem and understand the operation before he can use it regularly without assistance.h. Differentiation:

Content: The student completes all of the normal class activities. Extra attention is given to ensure that he understands the material during instruction.

Process: Student is grouped near stronger students so that during class time given to discussion he can voice his concerns to strong students who can clarify his questions in multiple ways. Student is also keep near strong students so that he has less opportunity to get distracted during instruction in side conversations.

Product: The student completes all normal class assessments.

Affect: Student receives private tutoring in math outside of class and we provide his tutor with material being covered in class to align his tutoring instruction with the class activities. Student work is also discussed with the student every week when he completes his athletic progress report for his after school sport.

Learning Environment: Student is grouped near strong students so that he can ask clarifying questions and to lessen his opportunities to get distracted by side conversations during class. Student is allowed to take his assessments in collaborative area to lessen his distraction.

i. Assessment: All students are given formative assessments daily during the unit to ensure that they understand the material and are making progress. Considering the remediation that Cody needs we make an effort to check his work everyday before he leaves to ensure that he understands the method before he tries to use it at home when completing his homework.

#4 Student – Average Level Studenta. Name: Kevinb. Need: Kevin didn’t turn in his homework during the first two weeks of class and has been spending the last 5 weeks raising his grade. c. Identity: Kevin is a 10th grade student. His primary language is English. He received a C during the first semester and an F in the second semester of Algebra 1 last year.d. Goals: Student wants to pass the class and attend Palomar Community College. He doesn’t have specific goals for after school.e. Readiness: The student understands the material currently being covered however he makes regular mistakes when working through problems. He needs to practice checking his work before moving on to the next problem. f. Interest: Kevin enjoys football but is not on the school team. g. Learning Profile: Kevin understands the material and only needs to be shown the methods to remember how to finish problems.h. Differentiation:

Content: Student completes all normal assignments

Process: Student is bringing up his grade to make up for not turning in homework during the first two weeks.

Product: Student completes all normal assessments in class.

Affect: Students work is addressed weekly to ensure that he in improving.

Learning Environment: Student completes all regular class activities.

i. Assessment: Student completes all normal classroom activities and assessments. He is monitored to make sure that he turns in his homework and continues to raise his grade.

#5 Student – High Level Studenta. Name: Aceb. Need: This student needs to be challenged to stay motivated during class and to stay on task during individual work. c. Identity: 9th grader. Primary language English.d. Goals: Student plans to attend College. He is currently on the freshmen football team and plans to play in sports every semester.e. Readiness: Student is proficient in all material covered so far in class. f. Interest: Student is interested in sports and maintaining his academic levels to stay on the team. g. Learning Profile: The student already understand much of the material covered in class and usually only needs to be let loose to finish the work. Care must be taken to check his work and to ensure that he finished his steps properly as he sometimes makes mistakes when going to fast.h. Differentiation:

Content: I usually move around the class during individual practice time and will ask Ace to clarify his steps and explain why he used specific processes in his answers if I see that he is done before other students.

Process: Ace completes all normal class activities. He is individually challenged when I see that he has completed work before other students to ensure that he stays on task for the entire lesson.

Product: Ace completes all normal class assessments and his work is looked at for clear thought and justification. Since he can finish the problems before most students I make sure that he checks his work to lessen the amount of fixable mistakes and to help him establish good mathematical habits.

Affect: Ace receives feedback on his performance during class when I walk around and address students.

i. Assessment: Student completes all normal classroom activities and assessments with the class. He is monitored to make sure that he doesn’t make mistakes when finishing problems as he has issues with trying to finish the problems too fast.

2. Unit Rationale: Enduring Understandings & Essential QuestionsThis unit introduces students to methods for solving systems of linear equations. These methods are practical uses of material covered up to this point in the unit. They can be used to quickly find intersections of feasible regions. These methods are also needed for solving more complex problems in later sections of mathematics.

Enduring Understandings (EU)Students will understand that there are multiple methods for solving systems of linear equations.Students will understand how to choose the best method for solving a given system of equations.

Essential QuestionsCan these methods always be used to solve systems of equations?What restrictions if any are their for solving these systems?

3. STANDARDS Content & Common Core Standards

A.REI.5 - Prove that, given a system of two equations in two variable, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

A.REI.6 - Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

A.REI.12 - Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

ELD Standard 3. Supporting opinions and persuading others -- Bridging Level: Negotiate with or persuade others in conversations in appropriate registers (e.g., to acknowledge new information in an academic conversation but then politely offer a counterpoint) using a variety of learned phrases, indirect reported speech (e.g., I heard you say X, and I haven’t thought about that before. However . . .), and open responses to express and defend nuanced opinions.

4. UNIT OBJECTIVES Student will be able to write and solve systems of linear equations. Students will graph systems of linear equations. Students will find solutions to systems algebraically. Students will extend their understanding of graphing systems of equations to explain the purpose and process for solving systems algebraically.Students will apply their knowledge to a real world situations in which they must write and solve systems of equations and inequalities to model a shopping trip.

5. ASSESSMENT PLANMonday

Diagnostic Assessment

Formality: formal

Purpose: diagnostic

Implementation Method: written examination

Communication of Expectations: explanation of purpose for assessment will be given before assessment.

Evaluation Criteria: Provided

Answer key on the document camera

Student Self-Assessments: Provided

Tuesday

Monitored independent practice

Formality: informal

Purpose: formative

Implementation Method: performance of students during independent practice.

Communication of Expectations:

Evaluation Criteria: Students are able to successfully complete the assignment and answer questions during class.

Cognitive: Students will understand why a system of linear equations can have 0,1, or infinitely many solutions. Students can explain what conditions are required for each of these states. Students will understand how graphs can used to visually express equations and assist in finding solutions.

Language Development: Students will be introduced to the concept of systems of linear equations. They will know the definition of systems of linear equations and solutions of a system of linear equations.

STUDENT ACTIVITY

Introductory Set: Students are asked to graph a series of linear equations on a graph. Student are asked to identify the intersection of two equations. Students are asked to describe how they found the intersection and explain how they proved that their chosen point was the intersection.

Guided Practice - Notes/Worksheet: Students will follow along on their worksheets while the instructor goes through the steps for solving a system of linear equations through graphing.

Independent Practice - Notes/Worksheet: Students will continue to fill out the worksheet and express what steps they are taking at each step. Students will practice describing their steps as they work through the problems.

ASSESSMENT

Diagnostic for the unit: Student will be monitored throughout the independent practice portion to check for understanding. Students will talk to their neighbors to check answers and clarify ideas.(Informal)

Summative for the day: Students will be randomly chosen by equality stick method to walk the class through their solution to the first page. Students will continue work on their worksheet for homework. (Informal)

Day 2 – Solving Systems of Linear Equations by Substitution

STANDARDS

Common Core Standard: A.REI.6 - Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Cognitive: Students will understand how to find the solution to a system of linear equations through the Substitution method.

Language Development: This lesson builds on previously learned vocabulary for describing linear equations. Students will be introduced to the Substitution method and understand what process it describes.

STUDENT ACTIVITY

Warm-up: Students will solve warm-up problem using the method of graphing demonstrated the day before. Students will go over their homework answers.

Guided Practice - Notes/Worksheet: Students will follow along on their worksheets while the instructor goes through the steps for solving a system of linear equations through substitution.

Independent Practice - Notes/Worksheet: Students will continue to fill out the worksheet and express what steps they are taking at each step. Students will practice describing their steps as they work through the problems.

ASSESSMENT

Diagnostic for the day: Student will be monitored throughout the independent practice portion to check for understanding. Students will talk to their neighbors to check answers and clarify ideas.(Informal)

Summative for the day: Students will be randomly chosen by equality stick method to walk the class through their solution to the first page. Students will continue work on their worksheet for homework. (Informal)

Day 3 – Solving Systems of Linear Equations by Elimination

STANDARDS

Common Core Standard: A.REI.6 - Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Cognitive: Students will understand how to use the elimination method to solve a system of linear equations. Students will recognize when this method is possible by examining the systems under consideration.

Language Development: This lesson builds on previously learned vocabulary for describing linear equations. Students will be introduced to the Elimination method and understand what process it describes.

STUDENT ACTIVITY

Warm-up: Students will solve warm-up problem using the method of substitution demonstrated the day before. Students will go over their homework answers.

Guided Practice - Notes/Worksheet: Students will follow along on their worksheets while the instructor goes through the steps for solving a system of linear equations through elimination.

Independent Practice - Notes/Worksheet: Students will continue to fill out the worksheet and express what steps they are taking at each step. Students will practice describing their steps as they work through the problems.

Review - Worksheet: Student will work through the worksheet utilizing all of the methods shown so far. Students will express conditions for the use of different methods and situations where multiple methods can be used. When multiple methods can be used students will explain and justify reasoning for their choice of method.

ASSESSMENT

Diagnostic for the day: Student will be monitored throughout the independent practice portion to check for understanding. Students will talk to their neighbors to check answers and clarify ideas.(Informal)

Summative for the day: Students will be randomly chosen by equality stick method to walk the class through their solution to the first page. Students will continue work on their worksheet for homework. (Informal)

Day 4 – Review for unit quiz

STANDARDS

Common Core Standard: A.REI.6 - Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Cognitive: Students will demonstrate understanding of methods for solving a systems of linear equations. Students will recognize when a specific method is possible by examining the systems under consideration. Students will understand how to choose between methods for solving systems of linear equations.

Warm-up: Students will solve warm-up problem using the method of elimination demonstrated the day before. Students will go over their homework answers.

Guided Practice: Students will answer questions concerning methods for solving systems of linear equations. Students will be called on to answer questions on the board and justify reasoning on the board for mathematical steps they take.

Independent Practice - Review Worksheet: Students work on a worksheet and express what steps they are taking at each step. Students will practice describing their steps as they work through the problems.

Review - Worksheet: Student will work through the worksheet utilizing all of the methods shown so far. Students will express conditions for the use of different methods and situations where multiple methods can be used. When multiple methods can be used students will explain and justify reasoning for their choice of method.

ASSESSMENT

Diagnostic for the day: Student will be monitored throughout the independent practice portion to check for understanding. Students will talk to their neighbors to check answers and clarify ideas.(Informal)

Summative for the day: Students will be randomly chosen by equality stick method to walk the class through their solution to the first page. Students will continue work on their worksheet for homework. (Informal)

Day 5 – Unit quiz

STANDARDS

Common Core Standard: A.REI.6 - Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Warm-up: Students will solve warm-up problem using the method of elimination demonstrated the day before. Students will go over their homework answers.

ASSESSMENT

Formative for the unit: Quiz. (Formal)

Day 6 – Systems of Linear Inequalities

STANDARDS

Common Core Standard: A.REI.12 - Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Cognitive: Students will demonstrate understanding of methods for solving a systems of linear equations. Students will recognize when a specific method is possible by examining the systems under consideration. Students will understand how to choose between methods for solving systems of linear inequalities.

Language Development: This lesson the following vocabulary, system of linear inequalities, and solutions of a system of linear inequalities.

STUDENT ACTIVITY

Introductory Set - Notes/worksheet: Students are asked to draw a number line corresponding to a number of inequalities. Students are asked draw a single equation on a graph and plot 3 points on the plane. Students are given a linear inequality similar to the equant and text all three points to see if they satisfy the inequality.

Guided Practice - Notes/Worksheet: Students will follow along on their worksheets while the instructor goes through the steps for solving a system of linear inequalities through graphing.

Independent Practice - Notes/Worksheet: Students will continue to fill out the worksheet and express what steps they are taking at each step. Students will practice describing their steps as they work through the problems.

ASSESSMENT

Diagnostic for the day: Student will be monitored throughout the independent practice portion to check for understanding. Students will talk to their neighbors to check answers and clarify ideas.(Informal)

Summative for the day: Students will be randomly chosen by equality stick method to walk the class through their solution to the first page. Students will continue work on their worksheet for homework. (Informal)

Day 7 – Review for unit exam

STANDARDS

Common Core Standard: A.REI.6 - Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Cognitive: Students will demonstrate understanding of methods for solving a systems of linear equations. Students will recognize when a specific method is possible by examining the systems under consideration. Students will understand how to choose between methods for solving systems of linear equations.

Warm-up: Students will solve warm-up problem using the method of elimination demonstrated the day before. Students will go over their homework answers.

Guided Practice: Students will answer questions concerning methods for solving systems of linear equations. Students will be called on to answer questions on the board and justify reasoning on the board for mathematical steps they take.

Independent Practice - Review Worksheet: Students work on a worksheet and express what steps they are taking at each step. Students will practice describing their steps as they work through the problems.

Review - Worksheet: Student will work through the worksheet utilizing all of the methods shown so far. Students will express conditions for the use of different methods and situations where multiple methods can be used. When multiple methods can be used students will explain and justify reasoning for their choice of method.

ASSESSMENT

Diagnostic for the day: Student will be monitored throughout the independent practice portion to check for understanding. Students will talk to their neighbors to check answers and clarify ideas.(Informal)

Summative for the day: Students will be randomly chosen by equality stick method to walk the class through their solution to the first page. Students will continue work on their worksheet for homework. (Informal)

Day 8 – Unit exam

STANDARDS

Common Core Standard: A.REI.6 - Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. A.REI.12 - Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Warm-up: Students will solve warm-up problem using the methods demonstrated the day before. Students will go over their homework answers.

ASSESSMENT

Formative for the unit: Exam. (Formal)

ANTICIPATORY SETI will describe the project that we will be completing at the end of the unit. I will highlight how the specific model we will be discussing could be changed to represent different situations and how the steps involved in solving for our specific cases can be used to solve for many different systems.

CLOSUREStudents will have successfully finished the unit project and have demonstrated their understanding of unit material through completion of unit exam.

In what ways have you differentiated instruction to meet the varying needs of your students?

I have already pre-identified students who need specific assistance and aid before the unit began. I schedule time into the instructional plan everyday to allow me to check on those students to see that they are understanding the material and are making progress on mastering the concepts.

What strengths and possible limitations do you see in your plan?

The lesson plan is ambitious currently however I actually have some room to extend the unit by up to 2 days to make sure that all students understand the material.

What forms of data/evidence might you collect from this unit to measure its effectiveness?

I plan to collect daily data in the form of my formative assessments of students understanding as we move through the unit. The unit also allows for me to collect specific formal data on student performance during the unit quiz and examination.

What have you learned about yourself, students, your unit plan topic, and/or planning in general as a result of designing this unit plan? What do you know now that you didn't know at the start of this unit or program?

Making sure that I hit all the required information while still staying on the pacing guide is much harder than I expected. I’m wondering how some teachers are able to progress through units so quickly and I want to know how many of their students truly understand the material before the class moves to the next unit.

9. RUBRIC WITH SELF-ASSESSMENT

Highlight or circle the criteria on the unit plan rubric that describes your unit plan.

Turn in your self-assessed (highlighted/circled) rubric as an attachment to your unit plan.

If you did this unit plan with a partner, you should each score yourselves individually. You should also include at the bottom of the scoring guide an evaluation of how you and your partner worked together.